Rewrite in simplest terms: -(3c - 8)

The ratio of students to teachers at a school is 19 to 1 how many students are there in each total number of people

vladimir2022 [97]

Question:

The ratio of students to teachers at a school is 19 : 1. How many students are there in each total number of people?

A: 100 people

b. 280 people

c.440 people

d.760 people

Answer:

A )95 students and 5 teachers

B)266 students and 14 teachers

C)418 students and 22 teachers

D)722 students and 38 teachers

Step-by-step explanation:

A: 100 people

Ratio = 19 : 1

The sum of the ratio is 19 + 1 = 20

Scale factor = $\frac{100}{20}$

scale factor = 5

The number students is $19 \times 5$ = 95

The number of teachers is $1 \times 5$ = 5

b. 280 people

Ratio = 19 : 1

The sum of the ratio is 19 + 1 = 20

Scale factor = $\frac{280}{20}$

scale factor = 14

The number students is $19 \times 14$ = 266

The number of teachers is $1 \times 14$ = 14

c.440 people

Ratio = 19 : 1

The sum of the ratio is 19 + 1 = 20

Scale factor = $\frac{440}{20}$

scale factor = 22

The number students is $19 \times 22$ = 418

The number of teachers is $1 \times 22$ = 22

d.760 people

Ratio = 19 : 1

The sum of the ratio is 19 + 1 = 20

Scale factor = $\frac{760}{20}$

scale factor = 38

The number students is $19 \times 38$ = 722

The number of teachers is $1 \times 38$ = 38

5 0

4 years ago

Given 1+cosx\sinx+sinx\1+cosx=4, find a numerical value of one trigonometric function of x.

Len [333]

Answer:

Option d. $sin(x)=\frac{1}{2}$

Step-by-step explanation:

The complete question is

Given (1+cosx)/(sinx) + (sinx)/(1+cosx) =4, find a numerical value of one trigonometric function of x.

a. tanx=2

b. sinx=2

c. tanx=1/2

d. sinx=1/2

we have

$\frac{1+cos(x)}{sin(x)}+\frac{sin(x)}{1+cos(x)}=4$

Find the common denominator and adds the fractions

$\frac{(1+cos(x))^2+sin^2(x)}{(1+cos(x))sin(x)}=4$

Expanded the numerator

$\frac{(1+2cos(x)+cos^2(x)+sin^2(x)}{(1+cos(x))sin(x)}=4$

Remember that

$sin^2(x)+cos^2(x)=1$ ----> trigonometric identity

substitute

$\frac{1+2cos(x)+1}{(1+cos(x))sin(x)}=4$

$\frac{2+2cos(x)}{(1+cos(x))sin(x)}=4$

Factor 2 in the numerator

$\frac{2(1+cos(x))}{(1+cos(x))sin(x)}=4$

Simplify

$\frac{2}{sin(x)}=4$

$sin(x)=\frac{1}{2}$

7 0

3 years ago

PLEASE HELP ASAP!!! CORRECT ANSWER ONLY PLEASE!!!

lianna [129]

Answer: 1.61

==================================================

Work Shown:

tan(angle) = opposite/adjacent

tan(J) = IK/IJ

tan(J) = 45/28

tan(J) = 1.60714 approximately

tan(J) = 1.61

6 0

3 years ago

a trapezoid has an area of 20cm squared and a height of 5 cm. what is the sum of its top and bottom sides

bonufazy [111]

$A=\frac{a+b}{2} h$
A - area
h - height
a+b - sum of its top and bottom sides

$20=\frac{a+b}{2} \cdot 5 \\
4 = \frac{a+b}{2} \\
a+b=8$

The sum of its top and bottom sides is 8 cm.

6 0

3 years ago

Please help me with this!!!! Tyyyyyy

Anna35 [415]

Answer:

Step-by-step explanation:

I don't know what it's asking for but I assume what is angle B so we'll go with that. I think it's B 129 because it's right across from angle F which looks almost identical and is 130 degrees that's a 1 degree difference.

4 0

3 years ago

Rewrite in simplest terms: -(3c - 8) - 3c​

Rewrite in simplest terms: -(3c - 8) - 3c